Question

How much money should be deposited annually in a bank account for five years if you wish to withdraw ​$3 comma 000 each year for three​ years, beginning five years after the last​ deposit? The interest rate is 4​% per year.

Answer 1

Answer:

The five deposits will be for   $ 1,263.360

Explanation:

at the given rate of 4%

we are going to do 5 deposits.

Then, after 5 years we subtract 3,000 dollar during 3 years:

First, we solve for the PV of tat annuity:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 3,000.00

time 3

rate         0.04

$3000 \times \frac{1-(1+0.04)^{-3} }{0.04} = PV$

PV $8,325.2731

Then, we discount for the 5 years waiting period:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $8,325.2731

time  5.00

rate  0.04000

$\frac{8325.27309968139}{(1 + 0.04)^{5} } = PV$  

PV   6,842.7676

Now, we solve for which annuity of 5 deposits generates that amount:

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

FV 6,843

time 5

rate    0.04

$6842.76763180258 \div \frac{(1+0.04)^{5} -1 }{0.04} = C$

C  $ 1,263.360